Three hundred ninety-nine (399) HIV positive subjects will be enrolled in the study. This trial will be a Phase II, randomized partially blinded study evaluating the safety and efficacy of hydroxyurea when added to potent antiretroviral therapy in subjects with plasma HIV RNA already suppressed below the level of detection. The primary endpoints of the study will be loss of viral suppression (HIV RNA >=200 copies/ml) or study drug toxicity.